arXiv subjects

K. Sailer

Publications and source records attributed to K. Sailer.

At least 37 records · Page 2Linked to original sources

arXiv2010

Functional renormalization group for quantized anharmonic oscillator

Functional renormalization group methods formulated in the real-time formalism are applied to the $O(N)$ symmetric quantum anharmonic oscillator, considered as a $0+1$ dimensional quantum field-theoric model, in the next-to-leading order of the gradient expansion of the one- and two-particle irreducible effective action. The infrared scaling laws and the sensitivity-matrix analysis show the existence of only a single, symmetric phase. The field-independent term of the wavefunction renormalization turned out to be negligible, but its field-dependent piece is noticeable. It is shown that the infrared limits of the running couplings depend on the renormalization group scheme used, when the perturbation expansion in the bare quartic coupling is truncated keeping the terms up to the second order.

hep-th↗

arXiv2010

Phase Structure and Compactness

In order to study the influence of compactness on low-energy properties, we compare the phase structures of the compact and non-compact two-dimensional multi-frequency sine-Gordon models. It is shown that the high-energy scaling of the compact and non-compact models coincides, but their low-energy behaviors differ. The critical frequency $β^2 = 8π$ at which the sine-Gordon model undergoes a topological phase transition is found to be unaffected by the compactness of the field since it is determined by high-energy scaling laws. However, the compact two-frequency sine-Gordon model has first and second order phase transitions determined by the low-energy scaling: we show that these are absent in the non-compact model.

hep-th↗

arXiv2009

Comparison of renormalization group schemes for sine-Gordon type models

The scheme-dependence of the renormalization group (RG) flow has been investigated in the local potential approximation for two-dimensional periodic, sine-Gordon type field-theoric models discussing the applicability of various functional RG methods in detail. It was shown that scheme-independent determination of such physical parameters is possible as the critical frequency (temperature) at which Kosterlitz-Thouless-Berezinskii type phase transition takes place in the sine-Gordon and the layered sine-Gordon models, and the critical ratio characterizing the Ising type phase transition of the massive sine-Gordon model. For the latter case the Maxwell construction represents a strong constraint on the RG flow which results in a scheme-independent infrared value for the critical ratio. For the massive sine-Gordon model also the shrinking of the domain of the phase with spontaneously broken periodicity is shown to take place due to the quantum fluctuations.

hep-th↗

arXiv2009

Functional renormalization group approach to the sine-Gordon model

The renormalization group flow is presented for the two-dimensional sine-Gordon model within the framework of the functional renormalization group method by including the wave-function renormalization constant. The Kosterlitz-Thouless-Berezinski type phase structure is recovered as the interpolating scaling law between two competing IR attractive area of the global renormalization group flow.

hep-th↗

arXiv2007

Applicability of layered sine-Gordon models to layered superconductors: II. The case of magnetic coupling

In this paper, we propose a quantum field theoretical renormalization group approach to the vortex dynamics of magnetically coupled layered superconductors, to supplement our earlier investigations on the Josephson-coupled case. We construct a two-dimensional multi-layer sine-Gordon type model which we map onto a gas of topological excitations. With a special choice of the mass matrix for our field theoretical model, vortex dominated properties of magnetically coupled layered superconductors can be described. The well known interaction potentials of fractional flux vortices are consistently obtained from our field-theoretical analysis, and the physical parameters (vortex fugacity and temperature parameter) are also identified. We analyse the phase structure of the multi-layer sine--Gordon model by a differential renormalization group method for the magnetically coupled case from first principles. The dependence of the transition temperature on the number of layers is found to be in agreement with known results based on other methods.

cond-mat.supr-con↗

arXiv2007

Generalized universality in the massive sine-Gordon model

A non-trivial interplay of the UV and IR scaling laws, a generalization of the universality is demonstrated in the framework of the massive sine-Gordon model, as a result of a detailed study of the global behaviour of the renormalization group flow and the phase structure.

hep-th↗

arXiv2007

On the applicability of the layered sine-Gordon model for Josephson-coupled high-T_c layered superconductors

We find a mapping of the layered sine-Gordon model to an equivalent gas of topological excitations and determine the long-range interaction potentials of the topological defects. This enables us to make a detailed comparison to the so-called layered vortex gas, which can be obtained from the layered Ginzburg-Landau model. The layered sine-Gordon model has been proposed in the literature as a candidate field-theoretical model for Josephson-coupled high-T_c superconductors, and the implications of our analysis for the applicability of the layered sine-Gordon model to high-T_c superconductors are discussed. We are led to the conjecture that the layered sine--Gordon and the layered vortex gas models belong to different universality classes. The determination of the critical temperature of the layered sine-Gordon model is based on a renormalization-group analysis.

cond-mat.supr-con↗

arXiv2007

Renormalizable parameters of the sine-Gordon model

The well-known phase structure of the two-dimensional sine-Gordon model is reconstructed by means of its renormalization group flow, the study of the sensitivity of the dynamics on microscopic parameters. Such an analysis resolves the apparent contradiction between the phase structure and the triviality of the effective potential in either phases, provides a case where usual classification of operators based on the linearization of the scaling relation around a fixed point is not available and shows that the Maxwell-cut generates an unusually strong universality at long distances. Possible analogies with four-dimensional Yang-Mills theories are mentioned, too.

hep-th↗

arXiv2005

Renormalization-Group Analysis of Layered Sine-Gordon Type Models

We analyze the phase structure and the renormalization group (RG) flow of the generalized sine-Gordon models with nonvanishing mass terms, using the Wegner-Houghton RG method in the local potential approximation. Particular emphasis is laid upon the layered sine-Gordon (LSG) model, which is the bosonized version of the multi-flavour Schwinger model and approaches the sum of two ``normal'', massless sine-Gordon (SG) models in the limit of a vanishing interlayer coupling J. Another model of interest is the massive sine-Gordon (MSG) model. The leading-order approximation to the UV (ultra-violet) RG flow predicts two phases for the LSG as well as for the MSG, just as it would be expected for the SG model, where the two phases are known to be separated by the Coleman fixed point. The presence of finite mass terms (for the LSG and the MSG) leads to corrections to the UV RG flow, which are naturally identified as the ``mass corrections''. The leading-order mass corrections are shown to have the following consequences: (i) for the MSG model, only one phase persists, and (ii) for the LSG model, the transition temperature is modified. Within the mass-corrected UV scaling laws, the limit of J -> 0 is thus nonuniform with respect to the phase structure of the model. The modified phase structure of general massive sine-Gordon models is connected with the breaking of symmetries in the internal space spanned by the field variables. For the LSG, the second-order subleading mass corrections suggest that there exists a cross-over regime before the IR scaling sets in, and the nonlinear terms show explicitly that higher-order Fourier modes appear in the periodic blocked potential.

hep-th↗

arXiv2005

Differential Renormalization-Group Approach to the Layered sine-Gordon Model

New qualitative picture of vortex length-scale dependence has been found in recent electrical transport measurements performed on strongly anisotropic BSCCO single crystals in zero magnetic field. This indicates the need for a better description of the 3D/2D crossover in vortex dimensionality. The vortex-dominated properties of high transition temperature superconductors with extremely high anisotropy (layered systems) are reasonably well described in the framework of the layered XY model which can be mapped onto the layered sine-Gordon model. For the latter we derive an exact renormalization group (RG) equation using Wegner's and Houghton's approach in the local potential approximation. The agreement of the UV scaling laws find by us by linearizing the RG equations with those obtained previously in the literature in the dilute gas approximation makes the improvement appearant which can be achieved by solving our RG equations numerically.

hep-th↗

arXiv2004

Renormalization group in the internal space

Renormalization group in the internal space consists of the gradual change of the coupling constants. Functional evolution equations corresponding to the change of the mass or the coupling constant are presented in the framework of a scalar model. The evolution in the mass which yields the functional generalization of the Callan-Symanzik equation for the one-particle irreducible effective action is given in its renormalized, cutoff-independent form. The evolution of the coupling constant generates an evolution equation for the two-particle irreducible effective action.

hep-th↗

arXiv2004

Periodic ground state for the charged massive Schwinger model

It is shown that the charged massive Schwinger model supports a periodic vacuum structure for arbitrary charge density, similar to the common crystalline layout known in solid state physics. The dynamical origin of the inhomogeneity is identified in the framework of the bozonized model and in terms of the original fermionic variables.

hep-th↗

arXiv2003

Renormalization-Group Analysis of the Generalized sine-Gordon Model and of the Coulomb Gas for d >= 3 Dimensions

Renormalization-group (RG) flow equations have been derived for the generalized sine-Gordon model (GSGM) and the Coulomb gas (CG) in d >= 3 of dimensions by means of Wegner's and Houghton's, and by way of the real-space RG approaches. The UV scaling laws determined by the leading-order terms of the flow equations are in qualitative agreement for all dimensions d >= 3, independent of the dimensionality, and in sharp contrast to the special case d = 2. For the 4-dimensional GSGM it is demonstrated explicitly (by numerical calculations), that the blocked potential tends to a constant effective potential in the infrared (IR) limit, satisfying the requirements of periodicity and convexity. The comparison of the RG flows for the three-dimensional GSGM, the CG, and the vortex-loop gas reveals a significant dependence on the renormalization schemes and the approximations used.

hep-th↗

arXiv2002

Effective action and density functional theory

The effective action for the charge density and the photon field is proposed as a generalization of the density functional. A simple definition is given for the density functional, as the functional Legendre transform of the generator functional of connected Green functions for the density and the photon field, offering systematic approximation schemes. The leading order of the perturbation expansion reproduces the Hartree-Fock equation. A renormalization group motivated method is introduced to turn on the Coulomb interaction gradually and to find corrections to the Hartree-Fock and the Kohn-Sham schemes.

cond-mat.str-el↗

arXiv2002

Renormalization of the Periodic Scalar Field Theory by Polchinski's Renormalization Group Method

The renormalization group (RG) flow for the two-dimensional sine-Gordon model is determined by means of Polchinski's RG equation at next-to-leading order in the derivative expansion. In this work we have two different goals, (i) to consider the renormalization scheme-dependence of Polchinski's method by matching Polchinski's equation with the Wegner-Houghton equation and with the real space RG equations for the two-dimensional dilute Coulomb-gas, (ii) to go beyond the local potential approximation in the gradient expansion in order to clarify the supposed role of the field-dependent wave-function renormalization. The well-known Coleman fixed point of the sine-Gordon model is recovered after linearization, whereas the flow exhibits strong dependence on the choice of the renormalization scheme when non-linear terms are kept. The RG flow is compared to those obtained in the Wegner-Houghton approach and in the dilute gas approximation for the two-dimensional Coulomb-gas.

hep-th↗

arXiv2002

Functional Callan-Symanzik equation for QED

An exact evolution equation, the functional generalization of the Callan-Symanzik method, is given for the effective action of QED where the electron mass is used to turn the quantum fluctuations on gradually. The usual renormalization group equations are recovered in the leading order but no Landau pole appears.

hep-th↗

arXiv2001

Renormalization of composite operators

The blocked composite operators are defined in the one-component Euclidean scalar field theory, and shown to generate a linear transformation of the operators, the operator mixing. This transformation allows us to introduce the parallel transport of the operators along the RG trajectory. The connection on this one-dimensional manifold governs the scale evolution of the operator mixing. It is shown that the solution of the eigenvalue problem of the connection gives the various scaling regimes and the relevant operators there. The relation to perturbative renormalization is also discussed in the framework of the $ϕ^3$ theory in dimension $d=6$.

hep-th↗

arXiv2000

Response of an electron system to a periodic potential

We give a quantum field theoretical treatment of a one dimensional electron system with a fixed chemical potential $μ$. The non-perturbative Lindhard response function is found for an electron system in a sinusoidal potential.

hep-th↗